Stochastic Lagrangian models of velocity in homogeneous turbulent shear flow

Stochastic Lagrangian models for the velocity following a fluid particle are used both in studies of turbulent dispersion and in probability density function ~PDF! modeling of turbulent flows. A general linear model is examined for the important case of homogeneous turbulent shear flow, for which there are recent direct numerical simulation ~DNS! data on Lagrangian statistics. The model is defined by a drift coefficient tensor and a diffusion tensor, and it is shown that these are uniquely determined by the normalized Reynolds-stress and timescale tensors determined from DNS. With the coefficients thus determined, the model yields autocorrelation functions in good agreement with the DNS data. It is found that the diffusion tensor is significantly anisotropic—contrary to the Kolmogorov hypotheses and conventional modeling—which may be a low-Reynolds-number effect. The performance of two PDF models is also compared to the DNS data. These are the simplified Lagrangian model and the Lagrangian isotropization of production model. There are significant differences between the autocorrelation functions generated by these models and the DNS data. © 2002 American Institute of Physics. @DOI: 10.1063/1.1465421#